Vacuum structure and effective potential at finite temperature: a variational approach

We compute the effective potential for $\phi^4$ theory with a squeezed coherent state type of construct for the ground state. The method essentially consists in optimising the basis at zero and finite temperatures. The gap equation becomes identical to resumming the infinite series of daisy and super daisy graphs while the effective potential includes multiloop effects and agrees with that obtained through composite operator formalism at finite temperature.Comment: 15 pages, Revtex, No figures, to appear in Jou. of Phys.G(Nucl. and Part. Phys.

Chiral Symmetry Breaking and Pion Wave Function

We consider here chiral symmetry breaking through nontrivial vacuum structure with quark antiquark condensates. We then relate the condensate function to the wave function of pion as a Goldstone mode. This simultaneously yields the pion also as a quark antiquark bound state as a localised zero mode in vacuum. We illustrate the above with Nambu Jona-Lasinio model to calculate different pionic properties in terms of the vacuum structure for breaking of exact or approximate chiral symmetry, as well as the condensate fluctuations giving rise to $\sigma$ mesons.Comment: latex, revtex, 16 page

Secure state estimation against sensor attacks in the presence of noise

We consider the problem of estimating the state of a noisy linear dynamical system when an unknown subset of sensors is arbitrarily corrupted by an adversary. We propose a secure state estimation algorithm, and derive (optimal) bounds on the achievable state estimation error given an upper bound on the number of attacked sensors. The proposed state estimator involves Kalman filters operating over subsets of sensors to search for a sensor subset which is reliable for state estimation. To further improve the subset search time, we propose Satisfiability Modulo Theory-based techniques to exploit the combinatorial nature of searching over sensor subsets. Finally, as a result of independent interest, we give a coding theoretic view of attack detection and state estimation against sensor attacks in a noiseless dynamical system

Mesoscopic theory for fluctuating active nematics

Peer reviewedPublisher PD

Vector meson masses in hot nuclear matter : the effect of quantum corrections

The medium modification of vector meson masses is studied taking into account the quantum correction effects for the hot and dense hadronic matter. In the framework of Quantum Hadrodynamics, the quantum corrections from the baryon and scalar meson sectors were earlier computed using a nonperturbative variational approach through a realignment of the ground state with baryon-antibaryon and sigma meson condensates. The effect of such corrections was seen to lead to a softer equation of state giving rise to a lower value for the compressibility and, an increase in the in-medium baryonic masses than would be reached when such quantum effects are not taken into account. These quantum corrections arising from the scalar meson sector result in an increase in the masses of the vector mesons in the hot and dense matter, as compared to the situation when only the vacuum polarisation effects from the baryonic sector are taken into account.Comment: 13 pages revtex file, 6 figure

A microfluidic device for the study of the orientational dynamics of microrods

We describe a microfluidic device for studying the orientational dynamics of microrods. The device enables us to experimentally investigate the tumbling of microrods immersed in the shear flow in a microfluidic channel with a depth of 400 mu and a width of 2.5 mm. The orientational dynamics was recorded using a 20 X microscopic objective and a CCD camera. The microrods were produced by shearing microdroplets of photocurable epoxy resin. We show different examples of empirically observed tumbling. On the one hand we find that short stretches of the experimentally determined time series are well described by fits to solutions of Jeffery's approximate equation of motion [Jeffery, Proc. R. Soc. London. 102 (1922), 161-179]. On the other hand we find that the empirically observed trajectories drift between different solutions of Jeffery's equation. We discuss possible causes of this orbit drift.Comment: 11 pages, 8 figure